The radius of a planet is twice the radius of earth. Both have almost equal average
mass-densities. \(v_{p}\) and \(v_{e}\) are escape velocities of the planet and the earth, respectively, then

What should be the value of self-inductance of an inductor that should be connected to \(220 \mathrm{~V}\) \(50 \mathrm{~Hz}\) supply, so that a maximum current of \(0.9\) A flows through it?

Which of the following statement is true when a gamma decay occurs from the nucleus of an atom?

A source of alternating \(emf\ \varepsilon = \varepsilon_0\sin(\omega t)\) is connected to a capacitor. Then the instantaneous current in the circuit is:

In the normal adjustment of an astronomical telescope, the objective and eyepiece are 36 cm apart. If the magnifying power of the telescope is 8, find the focal lengths of the objective and eyepiece.

A car starts from rest and accelerates uniformly to a speed of \(180 \mathrm{kmh}^{-1}\) in \(10 \mathrm{~s}\). The distance covered by the car in this time interval is

For motion under central forces, which quantity will be conserved ?

Based on Crystal Field theory, match the Complex ions listed in Column I with the electronic configuration in the d orbitals of the central metal ion listed in Column II.

No.	Complex	No.	d orbital configuration of central metal ion
A	\([Mn(CN)_6]^{4-}\)	P	\(e_g^2 t_{2g}^3\)
B	\([Co(H_2O)_6]^{2+}\)	Q	\(t_{2g}^4 e_g^2\)
C	\([Fe(H_2O)_6]^{2+}\)	R	\(t_{2g}^5\)
D	\([MnCl_4]^{2-}\)	S	\(t_{2g}^5 e_g^2\)

The \(\mathrm{RMS}\) velocity of \(\mathrm{CH}_{4}, \mathrm{He}\) and \(\mathrm{SO}_{2}\) are in the ratio of

The figure shows a network of five capacitors connected to a 20 V battery. Calculate the charge acquired by each 10 \(\mu\)F capacitor.

Match the coordination compounds in Column I having the given type of hybridisation of \(\mathrm{M}^{\mathrm{n}+}\) ion and magnetic moment as given in Column II.
\(\begin{array}{|l|l|l|l|} \hline & \text { Coordination compounds. } & & \text { Hybridisation \& Magnetic nature. } \\ \hline \text { A } & \mathrm{Ni}(\mathrm{CO})_4 & \text { P } & \mathrm{sp}^3, \quad \mu=5.92 \mathrm{BM} \\ \hline \text { B } & {\left[\mathrm{Ni}(\mathrm{CN})_4\right]^{2-}} & \text { Q } & \mathrm{sp}^3, \quad \mu=2.84 \mathrm{BM} \\ \hline \text { C } & {\left[\mathrm{Ni}(\mathrm{Cl})_4\right]^{2-}} & \text { R } & \mathrm{sp}^3, \quad \mu=0 \\ \hline \text { D } & {[\mathrm{MnBr}]^{2-}} & \text { S } & \mathrm{dsp}^2, \quad \mu=0 \\ \hline \end{array}\)

The equation of the perpendicular drawn from the point \(A(6, 1, 3)\) to the line \(\dfrac{x-1}{2} = \dfrac{2-y}{-1} = \dfrac{z-3}{2}\) is \(\dfrac{x-6}{a} = \dfrac{y-1}{b} = \dfrac{z-3}{c}\). If \(a, b, c\) are the possible integers such that \(a < 0\), then the value of \(a - b + 5c\) is:

\(\int \frac{9^x}{\sqrt{1-81^x}} d x\) is equal to